# GaloisGroupUtilities RΒΆ

- R: Ring

GaloisGroupUtilities provides several useful functions.

- fillPascalTriangle: () -> Void
`fillPascalTriangle()`

fills the stored table.

- pascalTriangle: (NonNegativeInteger, Integer) -> R
`pascalTriangle(n, r)`

returns the binomial coefficient`C(n, r)=n!/(r! (n-r)!)`

and stores it in a table to prevent recomputation.

- rangePascalTriangle: () -> NonNegativeInteger
`rangePascalTriangle()`

returns the maximal number of lines stored.

- rangePascalTriangle: NonNegativeInteger -> NonNegativeInteger
`rangePascalTriangle(n)`

sets the maximal number of lines which are stored and returns the previous value.

- safeCeiling: R -> Integer if R has FloatingPointSystem
`safeCeiling(x)`

returns the integer which is greater than any integer with the same floating point number representation.

- safeFloor: R -> Integer if R has FloatingPointSystem
`safeFloor(x)`

returns the integer which is lower or equal to the largest integer which has the same floating point number representation.

- safetyMargin: () -> NonNegativeInteger if R has FloatingPointSystem
`safetyMargin()`

returns the number of low weight digits we do not trust in the floating point representation (used by safeCeiling).

- safetyMargin: NonNegativeInteger -> NonNegativeInteger if R has FloatingPointSystem
`safetyMargin(n)`

sets to`n`

the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by safeCeiling).

- sizePascalTriangle: () -> NonNegativeInteger
`sizePascalTriangle()`

returns the number of entries currently stored in the table.